{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:16:19Z","timestamp":1787328979012,"version":"build-2736575974"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11671302"],"award-info":[{"award-number":["11671302"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>In this paper, we present a two-level overlapping hybrid domain decomposition method for solving the large scale discrete elliptic eigenvalue problems. In order to eliminate the components in the orthogonal complement space of the eigenspace, we construct a parallel preconditioner for the eigenvalue problem in fine space. After one coarse space correction in each iteration, we get the error reduction as $\\gamma=c(1-C\\frac{\\delta}{H})$, where $C$ is a constant independent of the mesh size $h$ and the diameter of subdomains $H$, $\\delta$ is the overlapping size among the subdomains, and $c\\rightarrow1$ decreasingly as $H\\rightarrow0$, which means the greater the number of subdomains, the better the convergence rate. Different from other numerical algorithms in the literature, we do not need any assumptions between $H$ and $h$. Numerical results supporting our theory are given.<\/jats:p>","DOI":"10.1137\/16m1088302","type":"journal-article","created":{"date-parts":[[2018,1,24]],"date-time":"2018-01-24T10:32:45Z","timestamp":1516789965000},"page":"344-368","source":"Crossref","is-referenced-by-count":10,"title":["A Two-Level Overlapping Hybrid Domain Decomposition Method for Eigenvalue Problems"],"prefix":"10.1137","volume":"56","author":[{"given":"Wei","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xuejun","family":"Xu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,1,23]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1989-0962210-8"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/S1570-8659(05)80042-0"},{"key":"atypb3","volume-title":"Multigrid Methods","author":"Bramble J.","year":"1993"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/S106482759732678X"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827594261139"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1002\/nla.238"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970678"},{"key":"atypb8","first-page":"29","author":"D'yakonov E.","year":"1982","journal-title":"Vestnik Moskov. 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